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A note on centrality in 3-manifold groups

A note on centrality in 3-manifold groups
A note on centrality in 3-manifold groups
Centralizers in fundamental groups of 3-manifolds are well understood because of their relationship with Seifert fibre spaces. Jaco and Shalen's book [4] provides detailed information about Seifert fibre spaces in 3-manifolds, and consequently about centralizers in their fundamental groups. It is the purpose of this note to record two group-theoretic properties, both easily deduced from results of Jaco and Shalen. Doubtless many other authors could have established the same results had they needed them. Our motivation for writing this paper is that these properties can be used as a basis for group-theoretic proofs of certain fundamental results in 3-manifold theory: Proposition 1 below can be used as a basis for a proof of the Torus Theorem (cf. [8]) and Proposition 2 for the Torus Decomposition Theorem (cf. [9]).
0305-0041
261-266
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4

Kropholler, P.H. (1990) A note on centrality in 3-manifold groups. Mathematical Proceedings of the Cambridge Philosophical Society, 107 (2), 261-266. (doi:10.1017/S0305004100068523).

Record type: Article

Abstract

Centralizers in fundamental groups of 3-manifolds are well understood because of their relationship with Seifert fibre spaces. Jaco and Shalen's book [4] provides detailed information about Seifert fibre spaces in 3-manifolds, and consequently about centralizers in their fundamental groups. It is the purpose of this note to record two group-theoretic properties, both easily deduced from results of Jaco and Shalen. Doubtless many other authors could have established the same results had they needed them. Our motivation for writing this paper is that these properties can be used as a basis for group-theoretic proofs of certain fundamental results in 3-manifold theory: Proposition 1 below can be used as a basis for a proof of the Torus Theorem (cf. [8]) and Proposition 2 for the Torus Decomposition Theorem (cf. [9]).

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Published date: 1990
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 349622
URI: https://eprints.soton.ac.uk/id/eprint/349622
ISSN: 0305-0041
PURE UUID: 59dc7e6e-041f-41bd-9832-fbab753f80ca

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Date deposited: 12 Mar 2013 12:23
Last modified: 18 Jul 2017 04:40

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